Paul Manafort, a professional Republican political operative since the 1970s, was supposed to impose order on Donald J. Trump’s chaotic presidential campaign.

On Friday, the chaos devoured him.

Weeks of sliding poll numbers and false starts had sapped Mr. Manafort’s credibility inside the campaign. A cooling relationship with Mr. Trump — who had taken to calling Mr. Manafort “low energy,” the epithet he once used to mock a former rival, Jeb Bush — turned hot last weekend when the candidate erupted, blaming Mr. Manafort for a damaging newspaper article detailing the campaign’s internal travails, according to three people briefed on the episode.

Then a wave of reports about Mr. Manafort’s own business dealings with Russia-aligned leaders in Ukraine, involving allegations of millions of dollars in cash payments and secret lobbying efforts in the United States, threw a spotlight on a glaring vulnerability for Mr. Trump: his admiration for President Vladimir V. Putin of Russia.

By Friday morning, Mr. Manafort’s predictions to confidants that he might not be able to survive in his post had come true.

“This morning Paul Manafort offered, and I accepted, his resignation from the campaign,” Mr. Trump said in a statement. “I am very appreciative for his great work in helping to get us where we are today.”

In fact, Mr. Manafort did not go voluntarily. “My father just didn’t want to have the distraction looming over the campaign,” Eric Trump, the candidate’s second son, explained in a Fox News interview.

In a twist, Mr. Manafort’s ouster came after a week in which Mr. Trump had taken several steps toward the kind of normalized candidacy that Mr. Manafort had been striving for: The Republican nominee gave three speeches in which he generally stuck to a script; he mostly attacked Hillary Clinton, his Democratic opponent, while refraining from berating other Republicans; and, on Friday, he began running his first television advertisements.

The timing of Mr. Manafort’s departure largely overshadowed the news Thursday night when the candidate, who has long spurned apologies, announced at a rally that he actually regretted some of the more offensive things he has said — though without specifying which. And on Friday, Mr. Trump toured flood-ravaged areas of Baton Rouge, La., even as his aides were confirming Mr. Manafort’s exit.

Mr. Manafort, 67, who had managed national Republican conventions in the past, was hired in late March, as Mr. Trump was facing a pitched battle to amass the number of delegates needed to capture the party’s nomination. He was seen as a peer to Mr. Trump, 70, and as someone whose advice Mr. Trump might heed. He ended up taking the helm of the campaign when Corey Lewandowski, Mr. Trump’s previous campaign manager, was fired after repeatedly clashing with the candidate’s children.

Mr. Manafort helped defeat the “never Trump” movement within the Republican Party, opened lines of communication with party leaders in Washington and crushed a brief but noisy delegate uprising on the floor of the Republican convention in Cleveland on its first day. He also successfully pushed for the selection of Gov. Mike Pence of Indiana as Mr. Trump’s running mate.

But Mr. Trump never developed the sort of chemistry or comfort level with Mr. Manafort that he had with Mr. Lewandowski, campaign aides said. Mr. Trump has continued to seek out the advice of Mr. Lewandowski, who remains a fierce rival of Mr. Manafort.

Nor did Mr. Trump ever quite buy into what Mr. Manafort was selling.

Just as Mr. Trump has resisted behaving like a traditional presidential candidate, he has also felt little need to construct the sort of hierarchical organization typical of a campaign for the White House. This is in part, Mr. Trump’s advisers say, because he relies on his instincts and the counsel of his family. But it is also because he simply prefers to improvise, unconstrained by convention or by a chain of command.

A change in the leadership of his campaign may not stop Mr. Trump from making abrupt decisions based on news coverage, playing advisers off one another and following the guidance of whoever may be traveling with him or has just spoken to him on the phone.

But what Mr. Trump loses in Mr. Manafort is somebody who has had decades of experience in campaigns and relationships in the party that made him a useful ambassador for a candidate who lacks both, and is given to angering fellow Republicans.

Jason Miller, a spokesman for Mr. Trump, wrote on Twitter on Friday that Rick Gates, Mr. Manafort’s deputy, would leave New York for Washington, where he would serve as “the campaign’s liaison to the R.N.C.”

But it remains to be seen who will step into Mr. Manafort’s role of chief strategist for the final 11 weeks until Election Day.

Mr. Manafort’s exit came as Mr. Trump had been trying to reboot his campaign after a disastrous stretch in which he committed a series of self-inflicted wounds — belittling the mother of a Muslim soldier who was killed in Iraq and threatening to withhold an endorsement from House Speaker Paul D. Ryan, a fellow Republican. Aides have tried a range of efforts to rein in Mr. Trump’s impulses. But they have been unsuccessful in taming his propensity to respond sharply to media coverage of his campaign.

It was an article in The New York Times last weekend — about frequent but frustrated efforts by Mr. Trump’s top advisers to curtail his pugilistic instincts — that set off the series of events leading to Mr. Manafort’s departure.

On Saturday, Mr. Trump raged at Mr. Manafort, holding him responsible for the article, according to people familiar with the episode. On Sunday, Mr. Trump hastily convened a meeting of paid and unpaid advisers including the pollster Kellyanne Conway; Roger Ailes, the ousted Fox News chairman; and Stephen K. Bannon, the chairman of Breitbart News, a conservative website. Mr. Manafort was present for part of the meeting.

Mr. Ailes urged Mr. Trump to reconfigure the campaign’s leadership, according to a Republican briefed on the meeting. A former Republican strategist and ad man who was friends with Mr. Trump long before his ouster, Mr. Ailes had reviewed some of the initial television commercials Mr. Manafort had overseen and told Mr. Trump in blunt terms that they were lackluster.

Only on Tuesday was Mr. Manafort informed of the campaign’s impending shake-up, to be announced the next day: Ms. Conway would become campaign manager, and Mr. Bannon would become the campaign’s chief executive, according to a person with direct knowledge of the discussion.

At the same time, the new accounts of Mr. Manafort’s ties to Ukraine quickly eroded the support that he had from Mr. Trump’s family during his earlier battles with Mr. Lewandowski.

According to people briefed on the matter, Jared Kushner, Mr. Trump’s son-in-law, expressed increasing concern after a Times article published on Sunday about allegations of cash payments made to Mr. Manafort’s firm for his work on behalf of his main client, Viktor F. Yanukovych, the former Ukranian president, who is an ally of Mr. Putin.

Mrs. Clinton’s campaign has repeatedly sought to yoke Mr. Trump to Mr. Putin, citing Mr. Trump’s praise for the Russian leader. And the avalanche of stories about his work for pro-Russian entities in Ukraine were becoming untenable for the campaign, according to people briefed on the discussions.

“The easiest way for Trump to sidestep the whole Ukraine story is for Manafort not to be there,” said Newt Gingrich, the former House speaker who has become a counselor to Mr. Trump.

In North Carolina on Thursday, Mr. Trump was informed of the newest such report: an Associated Press article that, citing emails, showed that Mr. Manafort’s firm had orchestrated a pro-Ukrainian lobbying campaign in Washington without registering as a foreign agent.

That was enough, according to people briefed on the calls, for Mr. Trump to call Mr. Bannon and Ms. Conway.

He had the same message for each: It was time for Mr. Manafort to go.

Correction:

An earlier version of this article, and a news alert that linked to it, incorrectly described when Paul Manafort took the role of chief strategist for Donald J. Trump’s campaign. It happened on May 19, weeks before the firing of Corey Lewandowski, the campaign manager, not upon his firing.